How can object types be differentiated in the input of a neural network?
Neural networks learn. That's what they are for. For your task there are two sensible scenarios: 


You have a fixed reaction for danger and a fixed reaction for food and you only have to learn how to distinguish between them. In that case you basically try to classify the situation to trigger the right fixed response and this classification would be learned by backpropagation.
You directly learn to act for a given situation. In that case you can either use a genetic algorithm or you use reinforcement learning with backpropagation.


I would recommend using a genetic algorithm, because it is significantly easier and also makes sense in this situation. You would randomly initialise your network, let it run around in the environment and remember how much food it ate and how often or how quickly it died. Then you would randomly change the weights of your network and do the same thing again. If it did better this time around you would proceed to use the new weights otherwise you go back to the old weights and try a different random change. 
By selecting successful random changes it would over time learn to avoid danger and seek out food.

Edit: To my mind you have a fundamental misunderstanding how perception works. If you see a lion and a cake, do those trigger different kinds of cells on your retina? No! All nerve cells are used to detect all kinds of objects! The classification, i.e. whether you are seeing a lion or a cake happens in the neural network i.e. in the higher regions of your visual cortex, far removed from the initial nerve activation. Your lion might be yellow and your cake might be yellow, only if you analyse the high level structure of your nerve inputs can you decide what you are seeing. That is the task of a neural network. And that high level structure analysis is what a neural network learns. 

What seems to confuse you is the example you linked. In that example this very sparse distance measuring is enough to differentiate between walls and boosters in your high level structure analysis, because the different points of the walls that you sample have a certain relative position that you can analyse and conclude that they constitute the wall. 

In your scenario very sparse distance measuring will not help you obviously. The distance of an object doesn't tell you whether it's a lion or a cake. Distance and color would be a solution to that. Or, more realistically, you have different shapes and much tighter distance sampling, and high level analysis can work out the shape from a couple of closely measured distances.